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Symbolic product in Sage?

asked 2012-06-08 07:13:32 -0500

bk322 gravatar image

Suppose I'd like to compute

prod(1/x^4, x, 1, oo)

How can this be done?

I found an old thread, but with no answers.

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answered 2012-09-04 18:34:20 -0500

benjaminfjones gravatar image

Take the natural logarithm of your product and you get a sum which can be evaluated:

$$\ln\left( \prod_{x=1}^k \frac{1}{x^4} \right) = \sum_{x=1}^k \ln\left(\frac{1}{x^4}\right)$$

... now take the limit as $k \to \infty$:

sage: sum(ln(1/x^4), x, 1, oo)
sage: e^sum(ln(1/x^4), x, 1, oo)
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answered 2012-06-13 19:45:22 -0500

asteve gravatar image

updated 2012-06-13 20:04:51 -0500

Mike Hansen gravatar image

I found symbolic sum but not symbolic product in the reference files. I need to be able to classify a function of a erratic x which involve several symbolic foodstuffs from 1 to n or whatever. I then want to be able to do a derivative and a limit of this. I am trying out Sage because Mathematical doesn't seem to be able to handle this stuff exactly. I can define the function just fine but when I try to take the limit Mathematical can't seem to handle it.

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Am... Great, but why post it here?

bk322 gravatar imagebk322 ( 2012-06-14 04:23:20 -0500 )edit

answered 2012-09-03 21:00:32 -0500

I have the same problem. If someone know how to do

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Asked: 2012-06-08 07:13:32 -0500

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Last updated: Sep 04 '12